It is argued on general ground and demonstrated in the particular exam
ple of the Chiral Schwinger Model that there is nothing wrong with app
arently anomalous chiral gauge theory. If quantised correctly, there s
hould be no gauge anomaly and chiral gauge theory should be renormalis
able and unitary, even in higher dimensions and with nonabelian gauge
groups. Furthermore, mass terms for gauge bosons and chiral fermions c
an be generated without spoiling the gauge invariance.